Question

A rigid tank contains nitrogen gas at 227 °C and 100 kPa gage. The gas is heated until the gage pressure reads 250 kPa. If the atmospheric pressure is 100 kPa, determine the final temperature of the gas in °C.

Answer 1

The problem involves using Charles's Law, a form of the ideal gas law, to find the final temperature of nitrogen after heating, by converting all pressures to absolute pressures and applying the law to relate initial and final states.

Step-by-step explanation:

The student's question involves determining the final temperature of nitrogen gas in a rigid tank after heating, given initial temperature and pressures, using the ideal gas law. To solve this problem, we assume the nitrogen behaves as an ideal gas and use the relation between pressure, volume, temperature, and the number of moles of gas, which is constant since the tank is rigid.

Firstly, convert all pressures into absolute pressures by adding atmospheric pressure to the gage pressures. Then, apply the ideal gas law in the form of Charles's Law (P1/T1 = P2/T2), which relates pressure and temperature at constant volume and number of moles. To find the final temperature (T2), rearrange the equation to T2 = (P2/P1) * T1, where P2 and P1 are the final and initial absolute pressures, respectively, and T1 is the initial temperature in Kelvin.

Answer 2

T₂ =602 °C

Step-by-step explanation:

Given that

T₁ = 227°C =227+273 K

T₁ =500 k

Gauge pressure at condition 1 given = 100 KPa

The absolute pressure at condition 1 will be

P₁ = 100 + 100 KPa

P₁ =200 KPa

Gauge pressure at condition 2 given = 250 KPa

The absolute pressure at condition 2 will be

P₂ = 250 + 100 KPa

P₂ =350 KPa

The temperature at condition 2 = T₂

We know that

`(T_2)/(T_1)=(P_2)/(P_1)\\T_2=T_1* (P_2)/(P_1)\\T_2=500* (350)/(200)\ K\\`

T₂ = 875 K

T₂ =875- 273 °C

T₂ =602 °C