Gas Problem

Small potato

2015-04-01 8:33 pm

A cylinder contains a fixed mass of gas at a pressure of 10 Nm^-2 and a
temperature of 27 degree Celsius.

The cylinder is compressed to half of its original volume and the pressure increases to 3x10^5 Nm^-2

Find the final temperature of the gas

the answer is 177 degree Celsius
But i found the temp is very large

Thanks

回答 (1)

用戶26240

2015-04-01 9:03 pm

✔ 最佳答案

PV= nRT where n and R are constant.
PV/T = nR = constant
Hence, P1V1/T1 = P2V2/T2

Before compression : P1 = 10 N m⁻², T1 = 273 + 27 = 300 K, V1= V
After compression : P2 = 3 × 10⁵ N m⁻², T2 = ? K, V2 = (1/2)V

P1V1/T1 = P2V2/T2
10 × V / 300 = (3 × 10⁵) × (1/2)V / T2
Final temperature, T2 = 4.5× 10⁶ K

====
The initial pressure should be 10⁵ N m⁻² instead of 10 N m⁻².

Before compression : P1 = 10⁵ Nm⁻², T1= 273 + 27 = 300 K, V1 = V
After compression : P2 = 3 × 10⁵ N m⁻², T2 = ? K, V2 = (1/2)V

P1V1/T1 = P2V2/T2
10⁵ × V / 300 = (3 × 10⁵) ×(1/2)V / T2
Final temperature, T2 = 450K = (450 - 273)°C = 177°C

👍 0 👎 0