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The pressure, P, of a gas varies directly with its temperature, T, and inversely with its volume, V, according to the equation formula to find pressure, where n is the number of molar units and R is the universal gas constant. One molar unit of a gas has a pressure of about 1,245 joules at a temperature of 300 Kelvin and a volume of 2 liters. What is the pressure of the same number of molar units of the gas at a temperature of 400 Kelvin and a volume of 2.5 liters?

a)1,328 joules

b)1,900 joules

c)2,375 joules

d)2,600 joules

Verified Answer :

HomertheGenius

The equation formula:
P V = n R T
1,245 2 l = n R 300 K
n R = 1,245 2 : 300 = 8.3
P 2.5 l = n R 400 K
P 2.5 = 8.3 * 400
P = 3,320 : 2.5 = 1328 J
Answer:  A ) 1,328 joules.

As we know by ideal gas equation that

PV = nRT

here

n = number of moles

R = universal gas constant

T = temperature

P = pressure

V = volume

now here we have two set of data for same number of moles

so we will have

\(\frac{P_1V_1}{RT_1}= \frac{P_2V_2}{RT_2}\)

now we have

\(\frac{1245\times 2}{R(300)} = \frac{P_2(2.5)}{R(400)}\)

now we have to solve it for pressure

\(P_2 = \frac{1245\times 2 \times 400}{300\times 2.5}\)

\(P_2 = 1328 joules\)

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