Question

For an ideal gas,
A. the change in internal energy in a constant pressure process from temperature \[{{T}_{1}}\] to \[{{T}_{2}}\] is equal to \[n{{C}_{v}}({{T}_{2}}-{{T}_{1}})\], where \[{{C}_{v}}\] is the molar heat capacity at constant volume and n is the number of moles of the gas
B. The change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process.
C. The internal energy does not change in an isothermal process.
D. No heat is added or removed in an adiabatic process

Answer 1

Hint: Ideal gas is that gas which follows ideal gas laws under all conditions of temperature and pressure. There are many laws such as Boyle’s law, Charle’s law, Gay Loussac law etc. We are given with four statements and we have to determine which all are correct. There can be multiple correct answers here. Let us check all the statements one by one.

Complete answer:
Option A: The pressure remains constant, so this is an isobaric process. We know for an ideal gas the internal energy is independent of the pressure. Thus, U= \[n{{C}_{v}}({{T}_{2}}-{{T}_{1}})\] is always applicable for an ideal gas and this statement is correct.
Option B: We know that in an adiabatic process, there is no exchange of heat between the system and the surrounding. Now, from the first law of thermodynamics: \[dQ=dU+dW\]
Since no exchange of heat, \[dQ=0\]
Thus, \[dU=-dW\] or we can write \[\left| dU \right|=\left| -dW \right|\]
Thus, this statement is also correct.
Option C: In an isothermal process, the temperature remains constant. Thus, the change in internal energy will be zero. Hence, this statement is also correct.
Option D: Yes, in an adiabatic process there is no exchange of heat between the system and the surrounding.

Hence, all the statements are correct.

Note:The ideal gas law, also known as the general gas equation is an equation of state of a hypothetical ideal gas. Although the ideal gas law has several limitations, it is a good approximation of the behaviour of many gases under many conditions. The ideal gas law was stated by Benoit Paul Émile Clapeyron in 1834 as a combination of the empirical Charles’s law, Boyle’s Law, Avogadro’s law, and Gay-Lussac’s law.Ideal gas law, PV=nRT
\[P=\dfrac{nRT}{V}\]
We have used ideal gas law here because it was mentioned in the question that the gas is ideal. Otherwise we would have to use real gas laws.The three important parameters are pressure, temperature and the volume.