Question

A house has well-insulated walls. It contains a volume of 105 m3 of air at 305 K.

Consider heating it at constant pressure. Calculate the energy required to increase the temperature of this diatomic ideal gas by 0.7

Answer 1

Answer:
`85.46\ kJ`

Step-by-step explanation:

Given

Volume of air
`V=105\ m^3`

Temperature of air
`T=305\ K`

Increase in temperature
`\Delta T=0.7^(\circ)C`

Specific heat for diatomic gas is
`C_p=(7R)/(2)`

Energy required to increase the temperature is

`\Rightarrow Q=nC_pdT\\\\\Rightarrow Q=n* (7R)/(2)* \Delta T\\\\\Rightarrow Q=(7)/(2)nR\Delta T\\\\\Rightarrow Q=(7)/(2)* (PV)/(T)* \Delta T\quad [\text{using PV=nRT}]`

Insert the values

`\Rightarrow Q=(7)/(2)* (1.01325* 10^5* 105)/(305)* 0.7\\ \text{Assuming air pressure to be atmospheric P=}1.01325* 10^5\ N/m^2\\\\\Rightarrow Q=0.8546* 10^5\\\Rightarrow Q=85.46\ kJ`