An ideal gas undergoes an isothermal process from some initial state i to
the final state f.

(a) dU = 0 

(b) dQ = 0 

(c) dQ = dU 

(d) dQ = dW

Choose the correct alternatives:

1. (a, b, c)

2. (a, d)

3. (b, c, d)

4. (a, c, d)

(1, 4) Hint: In isothermal processes, the change in temperature is equal to zero.
Step 1: Find the change in the internal energy of the gas.
For an isothermal process change in temperature of the system, T =0  T =constant.
We know that for an ideal gas, dU = change in internal energy = nCvT = 0
[where n is the number of moles and C is the specific heat capacity at constant volume]
Step 2: Use the first law of thermodynamics.
From the first law of thermodynamics,
                             dQ = dU + dW
                                  = 0 + dWdQ = dW