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An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770C and a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cv of gas is
- a)0.718 kJ/kgK
- b)0.365 kJ/kgK
- c)0.319 kJ/kgK
- d)0.638 kJ/kgK
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature o...
Given, m =0.5 kg, p1 = p2 =600 kPa, T1 = 770C = 350 K, V1 = 0.08 m3, V2 = 0.12 m3, Q =2 kJ, W = −30 kJ
From ideal gas eqn,
p1V1 = mRT1
From ideal gas eqn,
p1V1 = mRT1
Most Upvoted Answer
An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature o...
Given information:
Mass of gas (m) = 0.5 kg
Initial pressure (P1) = 600 kPa
Initial temperature (T1) = 770°C = 1043K
Initial volume (V1) = 0.08 m³
Final pressure (P2) = 600 kPa
Final volume (V2) = 0.12 m³
Heat addition (Q) = 2 kJ
Work done on gas (W) = 30 kJ
We need to find the value of Cv for the gas.
The heat added to the gas can be given as:
Q = m * Cv * ΔT
where m is the mass of the gas, Cv is the specific heat capacity at constant volume, and ΔT is the change in temperature.
Rearranging the equation, we get:
ΔT = Q / (m * Cv)
The work done on the gas can be given as:
W = -P * ΔV
where P is the pressure and ΔV is the change in volume.
Rearranging the equation, we get:
ΔV = -W / P
Using the ideal gas law, we can relate the initial and final states of the gas:
P1 * V1 / T1 = P2 * V2 / T2
Rearranging the equation, we get:
T2 = T1 * (P2 * V2) / (P1 * V1)
Substituting the values, we get:
T2 = 1043K * (600 kPa * 0.12 m³) / (600 kPa * 0.08 m³) = 1564.5K
Now we can calculate the change in temperature:
ΔT = T2 - T1 = 1564.5K - 1043K = 521.5K
Substituting the values in the equation for Cv, we get:
ΔT = Q / (m * Cv)
521.5K = 2 kJ / (0.5 kg * Cv)
Cv = 2 kJ / (0.5 kg * 521.5K)
Simplifying the expression, we get:
Cv = 0.003831 kJ/kgK
Rounding off to three decimal places, the value of Cv is approximately 0.365 kJ/kgK.
Therefore, the correct answer is option B) 0.365 kJ/kgK.
Mass of gas (m) = 0.5 kg
Initial pressure (P1) = 600 kPa
Initial temperature (T1) = 770°C = 1043K
Initial volume (V1) = 0.08 m³
Final pressure (P2) = 600 kPa
Final volume (V2) = 0.12 m³
Heat addition (Q) = 2 kJ
Work done on gas (W) = 30 kJ
We need to find the value of Cv for the gas.
The heat added to the gas can be given as:
Q = m * Cv * ΔT
where m is the mass of the gas, Cv is the specific heat capacity at constant volume, and ΔT is the change in temperature.
Rearranging the equation, we get:
ΔT = Q / (m * Cv)
The work done on the gas can be given as:
W = -P * ΔV
where P is the pressure and ΔV is the change in volume.
Rearranging the equation, we get:
ΔV = -W / P
Using the ideal gas law, we can relate the initial and final states of the gas:
P1 * V1 / T1 = P2 * V2 / T2
Rearranging the equation, we get:
T2 = T1 * (P2 * V2) / (P1 * V1)
Substituting the values, we get:
T2 = 1043K * (600 kPa * 0.12 m³) / (600 kPa * 0.08 m³) = 1564.5K
Now we can calculate the change in temperature:
ΔT = T2 - T1 = 1564.5K - 1043K = 521.5K
Substituting the values in the equation for Cv, we get:
ΔT = Q / (m * Cv)
521.5K = 2 kJ / (0.5 kg * Cv)
Cv = 2 kJ / (0.5 kg * 521.5K)
Simplifying the expression, we get:
Cv = 0.003831 kJ/kgK
Rounding off to three decimal places, the value of Cv is approximately 0.365 kJ/kgK.
Therefore, the correct answer is option B) 0.365 kJ/kgK.
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An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer?
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An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer?.
An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer?.
Solutions for An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 770Cand a volume of 0.08 m3. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m3, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of Cvof gas isa)0.718 kJ/kgKb)0.365 kJ/kgKc)0.319 kJ/kgKd)0.638 kJ/kgKCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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