Question

4 moles of monoatomic ideal gas is compressed adiabatically causing the temperature to increase from 300 K to 400 K. Calculate the work done on the gas in units of Joules (if the answer is negative, be sure to enter a negative sign in your answer).

Answer 1

Answer:

the work done on the gas is 4,988.7 J.

Explanation:

Given;

number of moles of the monoatomic gas, n = 4 moles

initial temperature of the gas, T₁ = 300 K

final temperature of the gas, T₂ = 400 K

The work done on the gas is calculated as;

$W = \Delta U = nC_v(T_2 -T_1)$

For monoatomic ideal gas: $C_v = \frac{3}{2} R$

$W = \frac{3}{2} R \times n(T_2-T_1)$

Where;

R is ideal gas constant = 8.3145 J/K.mol

$W = \frac{3}{2} R \times n(T_2-T_1) \\\\W = \frac{3}{2} (8.3145) \times 4(400-300) \\\\W = \frac{3}{2} (8.3145) \times 4(100)\\\\W = 4,988.7 \ J$

Therefore, the work done on the gas is 4,988.7 J.