   Chapter 12, Problem 52P

Chapter
Section
Textbook Problem

A sealed container holding 0.500 kg of liquid nitrogen at its boiling point of 77.3 K is placed in a large room at 21.0°C. Energy is transferred from the room to the nitrogen as the liquid nitrogen boils into a gas and then warms to the room’s temperature. (a) Assuming the room’s temperature remains essentially unchanged at 21.0°C, calculate the energy transferred from the room to the nitrogen. (b) Estimate the change in entropy of the room. Liquid nitrogen has a latent heat of vaporization of 2.01 × 105 J/kg. The specific heat of N2 gas at constant pressure is C N 2 = 1.04 × 103J/kg · K.

(a)

To determine
The energy transferred from the room to the nitrogen.

Explanation

Given Info:

The mass of liquid nitrogen is 0.500kg .

Boiling point of nitrogen is 77.3K .

Room temperature is 21.0°C .

Latent heat of vaporization of liquid nitrogen is 2.01×105J/kg .

Specific heat of N2 gas at constant pressure is 1.04×103J/kg.K .

The heat energy absorbed by the liquid nitrogen will be used first for converting the liquid nitrogen to the gas form. Then warm the nitrogen gas to the room temperature.

The change in temperature is,

ΔT=(21+273)K77.3K=216.7K

Formula to calculate the total energy transferred from room to nitrogen is,

Qtotal=mLv+mcpΔT

• m is mass of liquid nitrogen
• Lv is the latent heat of vaporization of liquid nitrogen
• , cp is the specific heat of nitrogen gas at constant pressure
• ΔT is the change in temperature

Substitute 0

(b)

To determine
The change in entropy of the room.

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