Question

The specific heat at constant volume for a monatomic argon is 0.075 kcal/kg-K, whereas its gram molecular specific heat is \[{C_v} = 2.98\,cal/molK\]. The mass of the argon atom is (Avogadro’s number \[ = 6.02 \times {10^{23}}\,molecules/mol\]
A.\[6.60 \times {10^{ - 23}}g\]
B.\[3.30 \times {10^{ - 23}}g\]
C.\[2.20 \times {10^{ - 23}}g\]
D.\[13.20 \times {10^{ - 23}}g\]

Answer 1

Hint: Heat energy is equal to mass multiplied by specific heat multiplied by the change in temperature.


Complete step by step solution:
Now let us state the formula for specific heat.
\[Heat\,Energy = (mass\,of\,object) \times (specific\,heat) \times (change\,in\,temperature)\]
The mass of one mole of argon atom is equal to the gram molecular specific heat divided by the specific heat. This is equal to:
\[ = \dfrac{{2.98g}}{{0.075\,mol}} = 39.733\,g/mol\]
Thus, the mass of one atom of argon is equal to:
Therefore, the working is:
Mass of one atom of argon \[ = \dfrac{{39.733}}{{6.02 \times {{10}^{23}}}}g\]
On simplifying the RHS we get,
Mass of one argon atom is \[ = 6.60 \times {10^{ - 23}}g\]
Therefore, the correct option is option (a) i.e. \[ = 6.60 \times {10^{ - 23}}g\]

Additional Information:
All of us know the meaning of heat and what it is referred to. But most of us do not know what specific heat means. Specific heat refers to the ratio of the quantity of heat that we require to raise the temperature of a body by one degree that we need to increase the temperature of an equivalent mass of liquid (water) by one degree. The term in a much narrower sense refers to the amount of heat, in calories, that we require to raise the temperature of one gram of a substance by one degree Celsius.

Note: Before solving the sum, we need to be able to comprehend the meaning of specific heat. Students also need to keep in mind the calculations as they are complex, and students often tend to make a lot of mistakes in it.