An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature.

A. The work done by gas during the process is zero. 

B. The heat added to gas is different from change in its internal energy. 

C. The volume of the gas is increased. 

D. The internal energy of the gas is increased. 

E. The process is isochoric (constant volume process) Choose the correct answer from the options given below:

Use ideal gas law:

$$PV=nRT$$

Given pressure increases linearly with temperature,

$$P∝T$$

or

$$\frac{P}{T}=\text{constant}$$

From ideal gas law,

$$\frac{P}{T}=\frac{nR}{V}$$

Since P/T is constant,

$$V=\text{constant}$$

So process is isochoric.

Hence statement E is true.

For isochoric process,

$$W=\int PdV=0$$

So A is true.

First law:

$$Q=\Delta U+W$$

Since

W=0

$$Q=ΔU$$

So B ("heat added is different from change in internal energy") is false.

Volume does not increase (constant), so C is false.

Pressure increases linearly with temperature, so temperature increases.

For ideal gas internal energy depends only on temperature, so internal energy increases.

D is true.

Correct statements:

A, D, E