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

63.5 °C

Step-by-step explanation:

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

`w=P* \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=(nRT)/(P)`

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

`\Delta V=(nR* \Delta T)/(P)`

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

`w=P* (nR* \Delta T)/(P)=nR* \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* 8.314\ J/ Kmol * (T_2-301.15\ K)`

Thus,

`T_2=301.15\ K+(1770)/(6* 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