A ‘thermacole’ icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of 5.0 cm. If 4.0 kg of ice is put in the box, estimate the amount of ice remaining after 6 h. The outside temperature is 45°C, and the co-efficient of thermal conductivity of thermacole is 0.01 J s–1 m–1 K–1. [Heat of fusion of water = 335 × 103 J kg–1]

Asked by Abhisek | 1 year ago |  183

##### Solution :-

Side of the cubical icebox, s =30 cm=3 x 10-2 m
Thickness of the icebox, L =5.0 cm=0.05 m
Mass of ice kept in the icebox, m=4 kg

Time, t=6 h=6×60×60 = 21600
Outside temperature, T1= 45°C

Temperature of the icebox = 0°C

Temperature difference = T1 – T2 =45°C – 0°C

Surface area of the icebox = 6 x (0.30)2= 0.54
Coefficient of thermal conductivity of thermacole, K=0.01 Js−1m−1k−1
Heat of fusion of water, L= 335×10 3 Jkg −1

Total heat entering the icebox in 6 hours is

Q = $$\dfrac{KA(T_1−T_2)t}{L}$$

$$\dfrac{(0.01 Js^{-1}m^{-1}C^{-1} \times 0.54 m^2 \times 450 C \times 21600 s)}{0.05 m}$$

= 1.05 x 105 J

Let m be the total amount of ice that melts in 6 h.

But Q= mL
Therefore, m = Q/L
=$$\dfrac{1.05 \times 10^5}{(335×10^3)}$$

=0.313 kg

Amount of ice remaining after 6 h

= 4–0.313

=3.687 kg

Answered by Pragya Singh | 1 year ago

### Related Questions

#### A hot ball cools from 90°C to 10°C in 5 minutes. If the surrounding temperature is 20°C

A hot ball cools from 90°C to 10°C in 5 minutes. If the surrounding temperature is 20°C, what is the time taken to cool from 60°C to 30°C?

#### At what temperature and pressure can the solid, liquid and vapour phases of CO2 co-exist in equilibrium?

Answer the following questions based on the P-T phase diagram of carbon dioxide:

(a) At what temperature and pressure can the solid, liquid and vapour phases of $$CO_2$$ co-exist in equilibrium?

(b) What is the effect of the decrease of pressure on the fusion and boiling point of $$CO_2$$?

(c) What are the critical temperature and pressure for $$CO_2$$? What is its significance?

(d) Is $$CO_2$$ solid, liquid or gas at

(a) –70°C under 1 atm,

(b) –60°C under 10 atm,

(c) 15°C under 56 atm?

#### A body cools from 80°C to 50°C in 5 minutes. Calculate the time it takes to cool from 60°C to 30°C

A body cools from 80°C to 50°C in 5 minutes. Calculate the time it takes to cool from 60°C to 30°C. The temperature of the surroundings is 20°C.

#### Explain why a body with large reflectivity is a poor emitter

Explain why :

(a) a body with large reflectivity is a poor emitter

(b) a brass tumbler feels much colder than a wooden tray on a chilly day

(c) an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open, but gives a correct value for the temperature when the same piece is in the furnace

(d) the earth without its atmosphere would be inhospitably cold

(e) heating systems based on the circulation of steam are more efficient in warming a building than those based on the circulation of hot water