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Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is:
Correct answer is between '3233,3325'. Can you explain this answer?
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Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L...
ans
W =q = 2.303RTlog V2/V1
=2.303 *1*2*1000*log 100/10
=4606cal
efficiency =T2-T1/T2=q2-q1/q2
=1-T1/T2=1-q1/q2
T1/T2=q1/q2
300/1000 =q1/4606
q1=1381.8cal
useful work obtained =
4606 -1381.1
=3224.2cal
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Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L...
Given:
- Number of moles of H2 gas (n) = 1 mole
- Initial volume (V1) = 10 L
- Final volume (V2) = 100 L
- Temperature (T) = 1000 K
- Sink temperature (Ts) = 300 K
Assumptions:
- The expansion of H2 gas is isothermal, meaning the temperature remains constant during the process.
- The expansion is reversible, meaning the gas expansion is carried out in infinitely small steps, allowing the system to be in equilibrium at all times.
Formula:
The work done during an isothermal reversible expansion can be calculated using the formula:
W = -nRT ln(V2/V1)
Where:
- W is the work done (in J)
- n is the number of moles of gas
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature (in K)
- ln is the natural logarithm function
- V1 and V2 are the initial and final volumes of the gas, respectively
Calculation:
Substituting the given values into the formula:
W = -1 * 8.314 * 1000 * ln(100/10)
W = -8314 * ln(10)
To convert the work from J to cal, we divide by the conversion factor 4.184 J/cal:
W_cal = (-8314 * ln(10))/4.184
W_cal ≈ -1985.68 cal
However, since work cannot be negative, the absolute value of the work is taken:
W_cal = 1985.68 cal
Final Answer:
The useful work obtained is approximately 1985.68 cal.
- Number of moles of H2 gas (n) = 1 mole
- Initial volume (V1) = 10 L
- Final volume (V2) = 100 L
- Temperature (T) = 1000 K
- Sink temperature (Ts) = 300 K
Assumptions:
- The expansion of H2 gas is isothermal, meaning the temperature remains constant during the process.
- The expansion is reversible, meaning the gas expansion is carried out in infinitely small steps, allowing the system to be in equilibrium at all times.
Formula:
The work done during an isothermal reversible expansion can be calculated using the formula:
W = -nRT ln(V2/V1)
Where:
- W is the work done (in J)
- n is the number of moles of gas
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature (in K)
- ln is the natural logarithm function
- V1 and V2 are the initial and final volumes of the gas, respectively
Calculation:
Substituting the given values into the formula:
W = -1 * 8.314 * 1000 * ln(100/10)
W = -8314 * ln(10)
To convert the work from J to cal, we divide by the conversion factor 4.184 J/cal:
W_cal = (-8314 * ln(10))/4.184
W_cal ≈ -1985.68 cal
However, since work cannot be negative, the absolute value of the work is taken:
W_cal = 1985.68 cal
Final Answer:
The useful work obtained is approximately 1985.68 cal.
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Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is:Correct answer is between '3233,3325'. Can you explain this answer?
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Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is:Correct answer is between '3233,3325'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is:Correct answer is between '3233,3325'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is:Correct answer is between '3233,3325'. Can you explain this answer?.
Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is:Correct answer is between '3233,3325'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is:Correct answer is between '3233,3325'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Heat obtained due to expansion of 1 mole of H2 gas at 1000 K from 10 L to 100 L under isothermal reversible condition is absorbed by an engine having a sink at 300 K. Useful work (cal) obtained is:Correct answer is between '3233,3325'. Can you explain this answer?.
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