When 400 J of heat are slowly added to 10 mol of an ideal monatomic gas, its temperature rises by 10°C. The work done on the gas is 845J.
The amount of work done on gas depends upon the internal energy change and the heat supplied to the system.
According to First Law of Thermodynamics, the change in internal energy is equal to the work done and the heat supplied to the system.
This is given by:
ΔU = W + Q
where, ΔU is change in Internal energy
W is the Work done
Q is the heat supplied
Given,
Q = 400J
Number of moles, n = 10
Change in temperature, ΔT = 10°C
Cv = 3/2R ; Since, the given gas is monoatomic (R=8.3)
We know that, ΔU = n Cv ΔT
On substituting the values in above formula,
ΔU = 10 × 3/2 × 8.3 × 10
ΔU = 1245J
Using,
ΔU = W + Q
1245J = W + 400
W = 845J
Hence, the work done on the gas is 845J.
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