Question

Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is 28.0 ∘C and the pressure is constant.Part AAs part of a machine design project, calculate the final temperature of the gas after it has done 1770 J .Express your answer using three significant figures.

Answer 1

Answer:

63.5 °C

Explanation:

The expression for the calculation of work done is shown below as:

$w=P\times \Delta V$

Where, P is the pressure

$\Delta V$ is the change in volume

Also,

Considering the ideal gas equation as:-

$PV=nRT$

where,  

P is the pressure

V is the volume

n is the number of moles

T is the temperature  

R is Gas constant having value = 8.314 J/ K mol

So,

$V=\frac{nRT}{P}$

Also, for change in volume at constant pressure, the above equation can be written as;-

$\Delta V=\frac{nR\times \Delta T}{P}$

So, putting in the expression of the work done, we get that:-

$w=P\times \frac{nR\times \Delta T}{P}=nR\times \Delta T$

Given, initial temperature = 28.0 °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T₁ = (28.0 + 273.15) K = 301.15 K

W=1770 J

n = 6 moles

So,

$1770\ J=6 moles\times 8.314\ J/ Kmol \times (T_2-301.15\ K)$

Thus,

$T_2=301.15\ K+\frac{1770}{6\times 8.314}\ K$

$T_2=336.63\ K$

The temperature in Celsius = 336.63-273.15 °C = 63.5 °C

The final temperature is:- 63.5 °C