Question

A cylinder with a moveable piston contains 92g of Nitrogen. The external pressure is constant at 1.00 atm. The initial temperature is 200K. When the temperature is increased by 83 K, by taking it out of the freezer, the volume will increase, according to the Ideal Gas Law. Calculate the work for this process. Express your answer in J.

Answer 1

Answer:

The work for the given process is (- 2263.4 J)

Explanation:

Given: Mass of nitrogen gas (N₂): w = 92 g, external pressure: P = 1 atm, Initial temperature: T₁ = 200 K, Final temperature: T₂ = 200 + 83 K = 283 K

Molar mass of N₂ gas: m = 28 g, Gas constant: R = 8.314 J.K⁻¹.mol⁻¹

The number of moles of N₂ gas = w ÷ m = 92 g ÷ 28 g/mol = 3.28 mole

To find the initial volume (V₁) and final volume (V₂), we use the ideal gas equation:

$PV =nRT$

$V_{1}=nRT_{1}\div P$  

$V_{2}=nRT_{2}\div P$  

So the Work: $W = - P \Delta V$  

$W = - P (V_{2} - V_{2}) = - P (\frac{nRT_{2}}{P} - \frac{nRT_{1}}{P})$  

$W = nRT_{1} - nRT_{2} = nR(T_{1} - T_{2})$  

$W = nR(T_{1} - T_{2})$  

$W = (3.28 mole)(8.314 J.K^{-1}.mol^{-1})(200 K - 283K)$

$W = (3.28)(8.314)(-83)$

$W = (- 2263.4 J)$

Therefore, the work for the given process: W = (- 2263.4 J)