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 decreased by 70 K, by putting it in a lower temperature freezer, the volume will decrease, according to the Ideal Gas Law. Calculate the work for this process.

Answer 1

Answer:

$W = 3542.7 J$

Explanation:

As per ideal gas law we know that

PV = nRT

so we have

$P = 1.01 \times 10^5 Pa$

$n = \frac{92}{28} = 3.28 moles$

T = 200 K

now we have

$(1.01 \times 10^5) V = 3.28 (8.31)(200)$

$V_1 = 0.054 m^3$

Now we know that if pressure remains constant

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

$\frac{0.054}{200} = \frac{V_2}{70}$

$V_2 = 0.0189 m^3$

Now work done in this process is given as

$W = P \Delta V$

$W = (1.01 \times 10^5)(0.054 - 0.0189)$

$W = 3542.7 J$