10 mole of ideal gas expands isothermally and reversibly from a pressure of 10 atm to 1 atm at 300 K. What is the heavisest mass which can lifted through a height of 100 meter by this gas?
10 mole of ideal gas expands isothermally and reversibly from a pressure of 10 atm to 1 atm at 300 K. What is the heavisest mass which can lifted through a height of 100 meter by this gas?
The correct option is B 58.55 kg
This is an interestesting question. We are going to assume that the entire work done by the gas in expansion can be used to lift the object.
To start off, let us first figure out the work done on the gas. We know that this an isothermal, reversible process. We can directly use this equation:
W = −nRTlnP1P1 = −10 × 8.314 × 300 × 2.303 × log(101) = −57441.42J
Also, since ALL the work done by this gas can be used to lift this object, if we assume the mass to be 'm', we can safely write down the following equation:
W = −mgh
This is a basic idea from physics, where 'g' is the acceleration due to gravity.
m × 9.81 × 100 = 57441.42
m = 58.55 kg
Protip: Use 25/3 as the R value and assume g to be equal to 10m/s2, you will get an approximate answer and solve this numerical pretty quickly!
58.55 kg
This is an interestesting question. We are going to assume that the entire work done by the gas in expansion can be used to lift the object.
To start off, let us first figure out the work done on the gas. We know that this an isothermal, reversible process. We can directly use this equation:
W = −nRTlnP1P1 = −10 × 8.314 × 300 × 2.303 × log(101) = −57441.42J
Also, since ALL the work done by this gas can be used to lift this object, if we assume the mass to be 'm', we can safely write down the following equation:
W = −mgh
This is a basic idea from physics, where 'g' is the acceleration due to gravity.
m × 9.81 × 100 = 57441.42
m = 58.55 kg
Protip: Use 25/3 as the R value and assume g to be equal to 10m/s2, you will get an approximate answer and solve this numerical pretty quickly!
