Answer:
7.7°K
Explanation:
Using pV = NkT = nRT
U = CvNkT = Cv nRT
where:
Cv is a constant dependent on temperature (e.g. equal to 3/2 for a monatomic gas for moderate temperatures)
U is the internal energy
p is the pressure
V is the volume
n is the amount of gas (moles)
R is the gas constant, 8.314 J·K^−1mol^-1
T is the absolute temperature
N is the number of particles
k is the Boltzmann constant, 1.381×10^−23 J·K^−1
In your first problem, the energy difference between heat absorbed by the gas and the work performed is the energy lost to heat. So
∆E = Cv nR∆T
where ∆T is the temperature change
∆T = ∆E / (Cv nR)
= (750-625) / (3/2)(1.3)(8.314)
= 7.71° K
