Question

A gas 'x' at 17 degree Celsius is heated it's pressure doubles and volume triples from the original pressure and volume . if the original volume is 1000 cc calculate the temperature to which it should be heated​

Answer 1

Answer:

Temperature = 1740.9 K

Explanation:

Given:

• Initial temperature of gas = 17°C
• Final pressure of the gas = Double the initial pressure
• Final volume of the gas = Triple the initial volume
• Original volume = 1000 cm³

To Find:

• Final temperature

Solution:

Convert the temperature from °C to K

17 °C = 290.15 K

By the ideal gas equation we know that,

$\sf \dfrac{P_1V_1}{T_1} =\dfrac{P_2V_2}{T_2}$

where P is the pressure, V is the volume and T is the temperature of the gas.

Substitute the data,

$\sf \dfrac{P_1\times 1000}{290.15} =\dfrac{2\times P_1\times 3\times V_1}{T_2}$

$\sf \dfrac{P_1\times 1000}{290.15} =\dfrac{2\times P_1\times 3\times 1000}{T_2}$

Cancelling 1000 P₁ on both sides,

$\sf \dfrac{1}{290.15} =\dfrac{2\times 3}{T_2}$

$\sf \dfrac{1}{290.15} =\dfrac{6}{T_2}$

Cross multiplying,

T₂ = 6 × 290.15

T₂ = 1740.9 K

Hence the temperature to which the gas should be heated is 1740.9 K.

Answer 2

Answer:

Given :-

Initial temperature of gas = 17°C

Final pressure of gas = Double the initial pressure

Final volume of gas = 3 × the initial volume

Original volume = 1000 cm³

To Find :-

Temperature to be heated

Solution :-

17⁰ C = 290.15 K

Now,

$\sf \dfrac{P_1 V_1}{T1} \: = \dfrac{P_1 V_2}{T1}$

P1 × 100/290.15 = 2 × P1 × 3 × V1/T2

P1 × 100/290.15 = 6 × P1 × 1000/T2

1/290.15 = 6 /T2

6(290.15) = T2

T2 = 1740.9 K