Two kg of a monoatomic gas is at a pressure of 4 × 104 N/m2 . The density of the gas is 8 kg /m3. What is the order of energy of the gas due to its thermal motion ?

Question

Two kg of a monoatomic gas is at a pressure of 4 × 104 N/m2 . The density of the gas is 8 kg /m3. What is the order of energy of the gas due to its thermal motion ? (A) 103 J (B) 105 J (C) 106 J (D) 104 J

Tardigrade Admin · Accepted Answer

Thermal energy of N molecule = N((3/2)kT) =(N/NA) (3/2)RT = (3/2)(nRT) =(3/2)PV =(3/2)P((m/8)) = (3/2) ×4×104 ×(2/8) =1.5 ×104 order will 104

Q. Two kg of a monoatomic gas is at a pressure of $4 \times 1 0^{4} N / m^{2}$ . The density of the gas is $8 k g / m^{3}$ . What is the order of energy of the gas due to its thermal motion ?

$1 0^{3}$ J

$1 0^{5}$ J

$1 0^{6}$ J

$1 0^{4}$ J

Thermal energy of N molecule
$= N (\frac{3}{2} k T)$
$= \frac{N}{N _{A}} \frac{3}{2} RT$
$= \frac{3}{2} (n RT)$
$= \frac{3}{2} P V$
$= \frac{3}{2} P (\frac{m}{8})$
$= \frac{3}{2} \times 4 \times 1 0^{4} \times \frac{2}{8}$
$= 1.5 \times 1 0^{4}$
order will $1 0^{4}$

Q. Two kg of a monoatomic gas is at a pressure of 4×104N/m2 . The density of the gas is 8kg/m3. What is the order of energy of the gas due to its thermal motion ?

103 J

105 J

106 J

104 J