An ideal gas expands quasi-statically and isothermally from a state with pressurepand volumeVto a state with volume 4V. How much heat is added to the expanding gas?

Q = PV(In 4)

Explanation:

We are told that the volume expands from V to a state with volume 4V.

Thus, initial volume is V and Final volume is 4V.

We want to find How much heat is added to the expanding gas.

For an isothermal process, the work done is calculated from;

W = nRT(In(V_f/V_i))

Where;

V_f is final volume

V_i is initial volume

Thus;

W = nRT(In(4V/V))

W = nRT(In 4)

Now, from ideal gas equation, we know that;

PV = nRT

Thus;

W = PV(In 4)

Now from first law of thermodynamics, we know that internal energy is zero and thus; Q = W

Where Q is quantity of heat

Thus;

Q = PV(In 4)