A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 ml to 375 ml at a constant temperature of 37.0oC. As it does so, it absorbs 208 J of heat. The values of q and w for the process will be ________. (R=8.314J/molK) (ln7.5=2.01)

From the thermodynamics equation, we have ΔU=q+w.
For an isothermal reversible expansion of an ideal gas, ΔU=0. Therefore, q = -w.
The work done in an isothermal reversible expansion is given by:
w = -nRTln(V2/V1)
Given:
n = 0.04 mol
R = 8.314 J/molK
T = 37.0oC = 310.15 K
V1 = 50.0 ml = 0.05 L
V2 = 375 ml = 0.375 L
ln(V2/V1) = ln(0.375/0.05) = ln(7.5) = 2.01
Substituting the values:
w = -(0.04 mol)(8.314 J/molK)(310.15 K)(2.01)
w = -208 J
Since q = -w, q = +208 J
Therefore, q = +208 J and w = -208 J