# Chapter 17 - Work, Heat, and the First Law of Thermodynamics - Exercises and Problems - Page 498: 23

A minimum of $3000~J$ of heat energy must be removed to liquify the nitrogen.

#### Work Step by Step

The heat energy $Q$ required to change the temperature of a substance is: $Q = m~c~\Delta T$ The heat energy $Q$ required to change the state of a substance is: $Q = m~L$ We can find the heat energy that must be removed to lower the temperature of the nitrogen and change it into a liquid. $Q = m~c~\Delta T-m~L$ $Q = (0.0070~kg)(1040~J/kg~C^{\circ})(-196~^{\circ}C-20^{\circ}C)-(0.0070~kg)(2.0\times 10^5~J/kg)$ $Q = -3000~J$ A minimum of $3000~J$ of heat energy must be removed to liquify the nitrogen.

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