Question: A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0ml to 375ml at a constant ...

Question

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0ml to 375ml at a constant temperature of 37.0 $^\circ C$ . As it does so, it absorbs 208J of heat. The values of q and w for the process will be________. (R=8.314 J/molK) (ln7.5=2.01)
a. q= -208J, w= -208J
b. q= -208J,w= +208J
c. q= +208J, w= +208J
d. q= +208J, w= -208J

Answer 1

Solution

In an isothermal process, the temperature of the system remains constant. Work done in reversible expansion condition can be calculated by the given formula:
${w_{rev}} = - nRT\ln \dfrac{{{V_f}}}{{{V_i}}}$

Complete answer:
The process mentioned in the question is reversible and isothermal: A reversible process is a process is a process whose direction can be returned to its original state by inducing infinitesimal changes to some property. Both the system and the surrounding returns to this original state, with no other changes anywhere else in the universe. It means both system and surrounding are returned to their initial state at the end of the reverse process. During the reversible process, all the changes in state that occur in the system are in thermodynamic equilibrium with each other.
In an isothermal process, the temperature of the system remains constant. As in the question the ideal gas expands at constant temperature of 37 $^\circ C$
As mentioned in the question, the system absorbs heat. Thus the value of q i.e. heat is +208 J. Here the positive sign indicates absorption of heat.
As the process is reversible and isothermal, in that condition reversible expansion work (w) is:
${w_{rev}} = - nRT\ln \dfrac{{{V_f}}}{{{V_i}}}$
Here n=0.04 mol
R= 8.314 J/molK
T=37 $^\circ C$ i.e. 310 K
Final volume=375 ml
Initial volume=50 ml
On putting the values in the formula:
${w_{rev}} = - 0.04x8.314x310x\ln \dfrac{{375}}{{50}}$
= -103.09 x ln7.5
=- 207.22 J
= -208 J approx.

Therefore, the value of q is +208 J and w is -208 J i.e. option (d) is correct.

Note:
Beware about the sign convention of heat and work. Ass system is absorbing heat from the surrounding, then the sign will be positive and if the system releases heat to the surrounding, then the sign will be negative.