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Question
One mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of 27∘C. If the work done during the process is 3 kJ, then final temperature of the gas is: (Cv=20 J/K)
One mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of 27∘C. If the work done during the process is 3 kJ, then final temperature of the gas is: (Cv=20 J/K)
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Solution
The correct option is B 150 K
Since the gas expands adiabatically (i.e., no change in enthalpy) so the internal energy is totally converted into work.
For the gas, Cv=20 J/K. Thus, 20 J of energy is required for 1∘ change in temperature of the gas.
internal energy change involved during the process i.e., work done =3 kJ=3000 J.
Change in temperature =300020K=150 K
Initial temperature =300 K
Since, the gas expands so the temperature decreases and thus final temperature is 300−150=150.
Hence, option B is correct
Since the gas expands adiabatically (i.e., no change in enthalpy) so the internal energy is totally converted into work.
For the gas, Cv=20 J/K. Thus, 20 J of energy is required for 1∘ change in temperature of the gas.
internal energy change involved during the process i.e., work done =3 kJ=3000 J.
Change in temperature =300020K=150 K
Initial temperature =300 K
Since, the gas expands so the temperature decreases and thus final temperature is 300−150=150.
Hence, option B is correct
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