Question

A container holds 1.0 g of argon at a pressure of 8.0 atm.

a. How much heat is required to increase the temperature by 100°C at constant volume?

b. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant pressure?

Short answer

The answer for (a) is $31.25J$and (b) is$59.9K$

Step-by-step solution

Description 

As per provided information:

A container holds 1.0 g of argon at a pressure of 8.0 atm.

Heat required for isobaric heating through the difference of temperature$∆T$of n moles is provided by:

$Q=n{C}_p∆T$

Result of finding the accurate heat and temperature 

The number of moles is provided as:

$n=\frac{m}{M}$

Thus, it can be written as:

$Q=\frac{m}{M}{C}_v∆T$

Argon's molar mass to be $M=40g/mol$as well as Argon's isochoric specific heat $C_v=12.5J/molK$

Thus, it can be written on the basis of numerics:

$Q=\frac{1}{40}·12.5·100=31.25J$

It can be stated the relation of giving heat needed for the heating of isochoric.

Thus, there can provide an increase in temperature $∆T_p$for the case of isochoric as:

$Q=n{C}_p∆T_p\Rightarrow \to ∆T_p=\frac{Q}{n{C}_p}$

Thus, it can be written as after analysing the expression for heat:

$∆T_p=\frac{n{C}_v∆T_v}{n{C}_p}=\frac{1}{\gamma }∆T_v$

Thus, on the basis of numerics:

$∆T_p=\frac{1}{1.67}·100=59.9K$

The answer for (a) is $31.25J$ and (b) is$59.9K$.