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One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.
- a)V ’ = 2 V ,T ’ = T/2
- b)V ’ = 8 V , T = T/4
- c)V ’ = 4 V ,T’ = 8T
- d)V’ = V/2 ,T’ = 2T
Correct answer is option 'B'. Can you explain this answer?
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' and T', then the new number of moles of gas can be calculated using the ideal gas law:
PV = nRT
where P is the pressure of the gas, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
Assuming that the pressure of the gas remains constant during the volume and temperature changes, we can write:
n' = (P V' / R T')
where n' is the new number of moles of gas, V' is the new volume, and T' is the new temperature.
To relate n and n', we can use the fact that the gas is ideal, which means that the number of moles is proportional to the volume and inversely proportional to the temperature:
n / V = n' / V'
n' = n (V' / V) (T / T')
Substituting the expression for n' from the ideal gas law, we get:
n (V' / V) (T / T') = (P V' / R T')
Simplifying, we get:
n' = n (V' / V) (T / T') (P / R)
Therefore, the new number of moles of gas is proportional to the ratio of the new and old volumes, the ratio of the new and old temperatures, and the pressure of the gas.
PV = nRT
where P is the pressure of the gas, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
Assuming that the pressure of the gas remains constant during the volume and temperature changes, we can write:
n' = (P V' / R T')
where n' is the new number of moles of gas, V' is the new volume, and T' is the new temperature.
To relate n and n', we can use the fact that the gas is ideal, which means that the number of moles is proportional to the volume and inversely proportional to the temperature:
n / V = n' / V'
n' = n (V' / V) (T / T')
Substituting the expression for n' from the ideal gas law, we get:
n (V' / V) (T / T') = (P V' / R T')
Simplifying, we get:
n' = n (V' / V) (T / T') (P / R)
Therefore, the new number of moles of gas is proportional to the ratio of the new and old volumes, the ratio of the new and old temperatures, and the pressure of the gas.
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One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.a)V ’ = 2 V ,T ’ = T/2b)V ’ = 8 V , T = T/4c)V ’ = 4 V ,T’ = 8Td)V’ = V/2 ,T’ = 2TCorrect answer is option 'B'. Can you explain this answer?
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One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.a)V ’ = 2 V ,T ’ = T/2b)V ’ = 8 V , T = T/4c)V ’ = 4 V ,T’ = 8Td)V’ = V/2 ,T’ = 2TCorrect 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 One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.a)V ’ = 2 V ,T ’ = T/2b)V ’ = 8 V , T = T/4c)V ’ = 4 V ,T’ = 8Td)V’ = V/2 ,T’ = 2TCorrect 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 One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.a)V ’ = 2 V ,T ’ = T/2b)V ’ = 8 V , T = T/4c)V ’ = 4 V ,T’ = 8Td)V’ = V/2 ,T’ = 2TCorrect answer is option 'B'. Can you explain this answer?.
One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.a)V ’ = 2 V ,T ’ = T/2b)V ’ = 8 V , T = T/4c)V ’ = 4 V ,T’ = 8Td)V’ = V/2 ,T’ = 2TCorrect 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 One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.a)V ’ = 2 V ,T ’ = T/2b)V ’ = 8 V , T = T/4c)V ’ = 4 V ,T’ = 8Td)V’ = V/2 ,T’ = 2TCorrect 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 One mole of an ideal monoatomic gas is kept in a volume V and is at temperature T. If the volume and temperature of the gas are respectively changed to V’ and T’ in such a way that the entropy of the gas is unchanged, then which of the following is correct.a)V ’ = 2 V ,T ’ = T/2b)V ’ = 8 V , T = T/4c)V ’ = 4 V ,T’ = 8Td)V’ = V/2 ,T’ = 2TCorrect answer is option 'B'. Can you explain this answer?.
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