Question

When 2 grams of fuel is completely burnt in excess of oxygen, the temperature of a calorimeter of thermal capacity 100 cal gram containing 2900 grams of water rises by 3°C. Find the calorific value.
(A) 3500 cal/g (C) 3900 cal/g (B) 4000 cal/g (D) 4500 cal/g 1​

Answer 1

The calorific value of the fuel is equal to 4500 cal/g. The correct option is (D) 4500 cal/g.

Given:

The mass of fuel used = 2 grams

The thermal capacity of the calorimeter = 100 cal °C⁻¹

The increase in the temperature of the water = 3°C

The mass of the water = 2900 grams

To Find:

→ The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of 1 gram of a substance by 1°C. If the mass of the body is 'm' and the specific heat capacity is 'c', the amount of heat supplied is 'Q' and the temperature change is ΔT then:

                                   $\boldsymbol{\therefore c=\frac{Q}{m\triangle T} }\\\\\boldsymbol{\therefore Q=mc\triangle T}$

→ The heat capacity of a substance is the amount of heat energy required to raise the temperature of the given substance by 1°C. If the heat capacity of the body is 's', the amount of heat supplied is 'Q' and the change in temperature is ΔT then:

                                    $\boldsymbol{\therefore s=\frac{Q}{\triangle T} }\\\\\boldsymbol{\therefore Q=s\triangle T}$

The thermal capacity of the calorimeter (s) = 100 cal °C⁻¹

The specific heat capacity of water (c) = 1 cal g⁻¹ °C⁻¹

The increase in the temperature of the water (ΔT) = 3°C

→ Let the total heat energy required for the process be 'Q'.

                               $\boldsymbol{\therefore Q=mc\triangle T+s\triangle T}\\\\\boldsymbol{\therefore Q = 2900\times1\times3+100\times3}\\\\\boldsymbol{\therefore Q=8700+300}\\\\\boldsymbol{\therefore Q=9000\:Calorie}$

Since the amount of heat energy required for the process is 9000 Calorie, therefore the heat energy released by the fuel is equal to 9000 Calorie.

→ The calorific value of a substance is the amount of heat released by the complete combustion of the unit mass of that substance. The S.I. unit of calorific value is J/kg.

∵ The mass of the fuel (m) is 2 grams and the amount of heat released (Q) is equal to 9000 calorie.

∴ The calorific value of the fuel will be given as:

                    $\boldsymbol{Calorific\:\:Value=\frac{Amount\:of\:Heat\:released(Q)}{Mass \:of\:the\:fuel(m)}}$

                    $\\\\\boldsymbol{Calorific\:\:Value=\frac{Q}{m}} \\\\\boldsymbol{Calorific\:\:Value=\frac{9000}{2}} \\\\\boldsymbol{Calorific\:\:Value=4500\:cal/g}$

The calorific value of the fuel comes out to be equal to 4500 cal/g. Hence the correct option is (D) 4500 cal/g.

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