Question

Two moles of hydrogen are heated at constant volume. The temperature of the gas has increased from $280K$ to $320K$. If the specific heat of hydrogen at constant volume is 10.183kj/kgk, find the amount of heat absorbed in KJ (Molecular weight of hydrogen = 2.016).
A. $1.642$
B. $2.12$
C. $1.821$
D. $1.12$

Answer 1

When substances or materials get heated, they gain the heat energy. The molecules or atoms of substance gain the kinetic energy due to which their speed increases. Thus when two bodies of different temperature come in contact with each other, heat energy is transferred from one body to another and heat always flows from the hotter body to the colder one. And this change in temperature of a material depends on its specific heat capacity.

Complete step by step answer:
Specific heat is the energy required to raise the temperature of 1 g of a substance by 1℃. To find the amount of heat we can use this formula:
$Q = m\times c\vartriangle T$ …………………....(i)
Here: Q is heat flow, m is mass of the substance ,C is specific heat, ∆T is temperature change

For calculating the value of heat we require the value of mass, specific heat, temperature change. From question we know the value of specific heat and temperature but don’t know the value of mass so firstly we calculate the value of mass by using this formula:
$n = \dfrac{m}{M} \\\ \Rightarrow m = nM \\\$
Here,
n = no. of moles, as per question the value of mole is 2, M = Molecular weight, as per question the value is 2.016 and m =mass
Put above values of n, M we get the value of mass (m) i.e.:
$m = 2\times 2.016 \\\ \Rightarrow m = 4.032\times {10^{ - 3}}kg \\\$

Now we find the value of m, already know the value of C and M. Put all these values in equation (i) we get:
c=10.183KJ
Now, change it into j. After changing we get c = 10183J
Temperature of the gas is increased from 280 K to 320 K that is (320-280 = 40).
$\vartriangle Q = \dfrac{{\left( {4.032\times {{10}^{ - 3}}} \right)\times 10183\times 40}}{{{{10}^3}}}$KJ
$\therefore \vartriangle Q =1.642KJ$

So that the amount of heat absorbed is 1.642KJ. Hence, the correct answer is Option A.

Note: Always remember that when a substance is either heated or cooled down, its temperature change i.e. ΔT, depends upon the mass of that material and the material from which it is being made. Thus, specific heat represents the dimensionless heat capacity at constant volume; it is generally a function of temperature due to intermolecular forces. The same relationship (i.e. heat energy and specific heat) can be utilised to calculate the heat being given out by a substance when it cools.