Chapter 14, Problem 7P

A water heater can generate 32,000 kJ/h. How much water can it heat from 12°C to 42°C per hour?

To determine

The amount of water that is heated by a water heater.

Answer to Problem 7P

Solution:

The amount of water that is heated by a water heater is 254 kg.

Explanation of Solution

Given:

  $Q$ is 32000 kJ/h

  $cp$ of water is 4186 J/kgK

  $m$ is to be determined

  $Tf$ is 42 C

  $Ti$ is 12 C

Formula Used: The formula used is the relation between temperature and specific heat from thermodynamics.

  $Q=mcp(Tf-Ti)$

Where,

  $Q$ is the heat transferred

  $cp$ is the specific heat

  $m$ is the mass

  $Tf$ is the final temperature

  $Ti$ is the initial temperature

Calculation:

The power is 32000 kJ/h.

The energy delivered per hour must be 32000 kJ or 32,000,000 J.

This energy will raise the temperature of water of mass $m$ per hour.

Inserting the given values in the heat capacity formula: $32000000=m(4186)(42-12)$

  $32000000=m(4186)(30)$

  $m=254$ kg

Conclusion:

254 kg of water is heated per hour.