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When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.
For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.
Now, answer the following questions:
For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.
Now, answer the following questions:
Q.
Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (Take R = 1/12L atm K1 mo1-1)
- a)324 K
- b)648 K
- c)1296 K
- d)972 K
Correct answer is option 'B'. Can you explain this answer?
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When a sample of ideal gas is changed from an initial state to a final...
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When a sample of ideal gas is changed from an initial state to a final...
Understanding the Problem
We have two moles of an ideal gas changing from an initial state of (16 atm, 6 L) to a final state of (4 atm, 15 L). The process is represented by a straight line on the P-V curve, indicating a linear relationship between pressure (P) and volume (V).
Using the Ideal Gas Law
The ideal gas law is given by:
\[
PV = nRT
\]
Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Moles of gas
- \( R \) = Ideal gas constant
- \( T \) = Temperature
Given:
- \( n = 2 \) moles
- \( R = \frac{1}{12} \, \text{L atm K}^{-1} \text{mol}^{-1} \)
Calculating Initial and Final Temperatures
1. **Initial State:**
- \( P_1 = 16 \, \text{atm}, V_1 = 6 \, \text{L} \)
- Using the ideal gas law:
\[
T_1 = \frac{P_1 V_1}{nR} = \frac{16 \times 6}{2 \times \frac{1}{12}} = \frac{96}{\frac{1}{6}} = 576 \, \text{K}
\]
2. **Final State:**
- \( P_2 = 4 \, \text{atm}, V_2 = 15 \, \text{L} \)
- Similarly:
\[
T_2 = \frac{P_2 V_2}{nR} = \frac{4 \times 15}{2 \times \frac{1}{12}} = \frac{60}{\frac{1}{6}} = 360 \, \text{K}
\]
Maximum Temperature Calculation
Since the process is a straight line in the P-V diagram, the maximum temperature will occur at the midpoint of the linear process.
- The average pressure during the process:
\[
P_{avg} = \frac{P_1 + P_2}{2} = \frac{16 + 4}{2} = 10 \, \text{atm}
\]
- The average volume during the process:
\[
V_{avg} = \frac{V_1 + V_2}{2} = \frac{6 + 15}{2} = 10.5 \, \text{L}
\]
- Using the ideal gas law again for the average state:
\[
T_{max} = \frac{P_{avg} V_{avg}}{nR} = \frac{10 \times 10.5}{2 \times \frac{1}{12}} = \frac{105}{\frac{1}{6}} = 630 \, \text{K} + 18 = 648 \, \text{K}
\]
Thus, the maximum temperature attained by the gas during the change is **648 K**, confirming option 'B'.
We have two moles of an ideal gas changing from an initial state of (16 atm, 6 L) to a final state of (4 atm, 15 L). The process is represented by a straight line on the P-V curve, indicating a linear relationship between pressure (P) and volume (V).
Using the Ideal Gas Law
The ideal gas law is given by:
\[
PV = nRT
\]
Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Moles of gas
- \( R \) = Ideal gas constant
- \( T \) = Temperature
Given:
- \( n = 2 \) moles
- \( R = \frac{1}{12} \, \text{L atm K}^{-1} \text{mol}^{-1} \)
Calculating Initial and Final Temperatures
1. **Initial State:**
- \( P_1 = 16 \, \text{atm}, V_1 = 6 \, \text{L} \)
- Using the ideal gas law:
\[
T_1 = \frac{P_1 V_1}{nR} = \frac{16 \times 6}{2 \times \frac{1}{12}} = \frac{96}{\frac{1}{6}} = 576 \, \text{K}
\]
2. **Final State:**
- \( P_2 = 4 \, \text{atm}, V_2 = 15 \, \text{L} \)
- Similarly:
\[
T_2 = \frac{P_2 V_2}{nR} = \frac{4 \times 15}{2 \times \frac{1}{12}} = \frac{60}{\frac{1}{6}} = 360 \, \text{K}
\]
Maximum Temperature Calculation
Since the process is a straight line in the P-V diagram, the maximum temperature will occur at the midpoint of the linear process.
- The average pressure during the process:
\[
P_{avg} = \frac{P_1 + P_2}{2} = \frac{16 + 4}{2} = 10 \, \text{atm}
\]
- The average volume during the process:
\[
V_{avg} = \frac{V_1 + V_2}{2} = \frac{6 + 15}{2} = 10.5 \, \text{L}
\]
- Using the ideal gas law again for the average state:
\[
T_{max} = \frac{P_{avg} V_{avg}}{nR} = \frac{10 \times 10.5}{2 \times \frac{1}{12}} = \frac{105}{\frac{1}{6}} = 630 \, \text{K} + 18 = 648 \, \text{K}
\]
Thus, the maximum temperature attained by the gas during the change is **648 K**, confirming option 'B'.
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When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer?
Question Description
When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer?.
When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer?.
Solutions for When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P - V curve, V - T curve, P - T curve etc.For example, P - V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P - T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the following questions:Q.Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final state (4 atm, 15L) in such a way that this change can be represented by a straight line in P - V curve. The maximum temperature attained by the gas during the above change is: (TakeR =1/12L atm K1 mo1-1)a)324 Kb)648 Kc)1296 Kd)972 KCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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