Chapter 2, Problem 2.1CP

Electrical current is passed through a resistor immersed in a liquid in an adiabatic container. The temperature of the liquid is varied by $\text{1}°\text{C}$. The system consists solely of the liquid. Does heat or work flow across the boundary between the system and surroundings? Justify your answer.

Interpretation Introduction

Interpretation:For the given system, whether the heat or work flow across the boundary between system and surroundings or not needs to be determined.

Concept Introduction:

An adiabatic procedure is one which takes place so vastly that no heat transfer takes placebetween the system, or within the system and surroundings.If the heat is added at constant volume the heat energy goes completely into increasing the internal kinetic energy of the substances.

Answer to Problem 2.1CP

On the resistor work is done and this work is done within the surrounding. The liquid’s temperature is changed by 1 ⁰C. Hence due to the variation in temperature between system and surroundings, the flow of heat takes place across the boundary between surrounding and system.

Explanation of Solution

Suppose there is an adiabatic system containing a heating water and coil against a constant atmospheric pressure P atm.

  

The temperature increases when electrical energy is introduced within the system. As per the law of thermodynamics when energy is removed, the same amount of energy gets back in additional form. Therefore,

  $\text{ΔU=dq+dW}$

Here,

  $\text{ΔU}$ = change in internal energy,

  $\text{dq}$ = heat change

  $\text{dW}$ = work completed.

Adiabatic container is the system that means that no heat is exchanged from the system as well as its surroundings.

  $\text{dq}$ = 0

Hence,

  $\text{ΔU}$ = $\text{dW}$

On the resistor work is done and it is done within the surroundings.

The liquid’s temperature is changed by 1 ⁰C. Hence due to the variation in temperature between system and surroundings, the flow of heat takes place across the boundary between surrounding and system.