A sealed cylinder in an industrial pneumatic lift contains 0.080\text{ m}^3 of gas at an i… — JAMB UTME

A sealed cylinder in an industrial pneumatic lift contains $0.080\text{ m}^3$ of gas at an initial pressure of $1.50 \times 10^5\text{ Pa}$ and a temperature of $27^\circ\text{C}$ . The piston compresses the gas to a final volume of $0.020\text{ m}^3$ , raising the pressure to $7.50 \times 10^5\text{ Pa}$ . What is the final temperature of the gas in degrees Celsius ( $^\circ\text{C}$ )?

Cevap: 102 °C

Cevap

The final temperature of the gas is

102^\circ\text{C}

Using the combined gas law

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

with absolute initial temperature

T_1 = 300\text{ K}

gives

T_2 = 375\text{ K}

. Subtracting

273

yields the final temperature of

102^\circ\text{C}

Adım Adım Çözüm

Convert initial temperature to absolute temperature (Kelvin)

T_1 = 27 + 273 = 300\text{ K}

Gas laws require thermodynamic temperature measured on the Kelvin scale.

Set up the Combined Gas Law equation

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

Relates initial and final states when pressure, volume, and temperature all change for a fixed mass of gas.

Calculate the final absolute temperature

T_2

T_2 = 300 \times \frac{7.50 \times 10^5 \times 0.020}{1.50 \times 10^5 \times 0.080} = 375\text{ K}

Evaluating the ratio of

P_2 V_2

P_1 V_1

yields

1.25

Convert final temperature from Kelvin to Celsius

\theta_2 = 375 - 273 = 102^\circ\text{C}

The question explicitly requires the answer in degrees Celsius.

Anahtar Kavram

Combined Gas Law and thermodynamic temperature conversion

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru