Answer to Question #163204 in Mechanical Engineering for Tarun.H.S

Question

Express one ton of refrigeration in terms of kJ/hour.

Answer 1

Q163204

Express one ton of refrigeration in terms of kJ/hour.

Solution:

One ton of Refrigeration: It is a unit of power used for describing the heat extracting capacity of refrigerators and Air conditioning equipment.

One ton Refrigeration is the amount of heat extracted per day for converting 1 ton (907 kg) of water at 0 ⁰C to Ice at 0 ⁰C.

The Heat of fusion of water is 334 J/g.

and 907 kg in grams $= 907 kg * \frac{1000g}{1kg} = 907,000 grams$

So for converting 907,000 g of water ( 0 ⁰C) to ice ( 0 ⁰ C), we will have to extract

Q = m * ΔH _fusion = 907,000 g * 334 J/g = 302,938,000 J.

So we need to extract 302,938,000 Joules of heat in a day for converting 1 ton ( 907g ) of

water at 0 ⁰C to ice at 0 ⁰C.

1-ton Refrigeration = 302,938,000 J / day.

We have to convert this to kJ / hour.

We will use the conversion factor 1kJ = 1000J and 1 day = 24 hours for converting

this to kJ/hour

1-ton refrigeration in kJ/hour $= \frac{302,938,000\space Joule}{1\space day}*\frac{1\space kJ}{1000\space J} * \frac{1\space day}{24\space hours }= 12,622 kJ/hour.$

So one-ton of refrigeration is equal to 12,622 kJ/hour.

(Note: In the USA 1 short ton (907 kg) is used for measuring one-ton refrigeration.

In some countries, 1 ton (1000 kg water ) is used for measuring one-ton refrigeration.

After plugging 1000 kg instead of 907 kg we will get 13,917 kJ/hr as the answer. )