Question

The temperature of a \[3Kg\] block of aluminium raised by $3$ degrees .How much heat would be needed to raise the temperature of a \[9Kg\] block of aluminium by $3$ degrees?
A. $9\,times$ As much heat as the \[3Kg\] block
B. $3\,times$ As much heat as the \[3Kg\] block
C. The same amount of heat as the \[3Kg\] block
D. one-third as much heat as the \[3Kg\] block
E. one-ninth as much heat as the \[3Kg\] block

Answer 1

Hint: In thermodynamics, specific heat of a substance is the minimum amount of heat required to raise the temperature of that substance by one degree Celsius and it’s denoted by $S$ . WE will use the general formula of relation between temperature raised and heat added to the system which is written as $Q = mS\Delta T$ where $m$ is the mass of the substance which is raised by a temperature of $\Delta T$ which has a specific heat value of $S$.

Complete step by step answer:
Let us assume that specific heat of aluminium is denoted by ${S_{Al}}$ and let ${Q_i}$ be the heat given to the block of aluminium with mass of ${m_i} = 3Kg$ with the increases in temperature as given in question is $\Delta T = {3^0}C$ now, using the formula $Q = mS\Delta T$ we have,
${Q_i} = {m_i}{S_{Al}}\Delta T$
On putting the values of given parameters we have,
${Q_i} = 9{S_{Al}} \to (i)$
Now, let us assume that the heat required to raise the temperature of a ${m_f} = 9Kg$ block of aluminium by $\Delta T = {3^0}C$ is denoted by ${Q_f}$ again, by using the formula $Q = mS\Delta T$ we have,
${Q_f} = {m_f}{S_{Al}}\Delta T$
On putting the values of given parameters we have,
${Q_f} = 27{S_{Al}}$
From equation ${Q_i} = 9{S_{Al}} \to (i)$ put the value of ${S_{Al}} = \dfrac{{{Q_i}}}{9}$ we get,
${Q_f} = 27 \times \dfrac{{{Q_i}}}{9}$
$\therefore {Q_f} = 3{Q_i}$
So, we will need twice the amount of heat to raise the \[9Kg\] block of aluminium by $3$ degrees.

Hence, the correct option is B.

Note: It should be remembered that, the value of specific heat of any substance which is denoted by $S$ is a fixed constant value for that particular substance and units of heat is used as Joules whereas the SI units of specific heat of a substance is given by $JK{g^{ - 1}}{C^{ - 1}}$ . And the value of specific heat is different for different materials.