when two object P and Q are supplied with the same quantity of heat, the temperature change in P is observed to be twice that of Q. The mass of P is half that of Q. The ratio of the specific heat capacity of P to Q

When two object P and Q are supplied with the same quantity of heat, the temperature change in P is observed to be twice that of Q. The mass of P is half that of Q. The ratio of the specific heat capacity of P to Q

Explanation:

Specific heat capacity

It is defined as amount of heat required to raise the temperature of a substance by one degree celsius.

It is given as:

Heat absorbed = mass of substance x specific heat capacity x rise in temperature

or,

Q = m x c x t

In above question, it is given:

For Q

mass of Q = m

Temperature changed = T₂/2

Heat supplied = x

Q = mc t

or

X=m x C₁ X T₁

or, X = m x C₁ x T₂/2

or, C₁=X x 2 / m x T₂ (equation 1)

For another quantity : P

mass of P = m/2

Temperature = T₂

Heat supplied is same that is : X

so, X = m/2 x C₂ x T₂

or, C₂=2X/m. T₂ (equation 2)

Now taking ratio of C₂ to c₁, We have

C₂/C₁ = 2X / m. T₂ / 2X / m. T₂

so, C₂/C₁ = 1/1

so, the ratio is 1: 1