Two 2 moles of monoatomic gas initially at 25c and 05 atm is...

TWO (2) moles of monoatomic gas initially at 25°C and 0.5 atm is compressed isothermally to 1.25 atm. If the gas behaves like an ideal gas, compute:i.the final volume of the gas(6 marks)ii.heat lost during compression

Transcript

00:01 So here in this problem we are given that two moles of monoatomic gas is initially at 25 degrees celsius that means n we have two and initial temperature t1 we have 25 degrees celsius that means 298 kelvin after adding to 73 we'll get the value in kelvin so 298 kelvin and initial pressure we are given as 0 .5 a tm and and if you convert this thing into kiosk will get 50 .66 kilopascal and it is compressed isothermally that means t1 and t2 is same here to 1 .25 a tm so pressure p2 becomes 1 .25 atm and we have to calculate two things first we have to calculate the final volume v2 and second we have to calculate the heat lost during compression so q we have to calculate so we'll be proceeding with the solution first we'll be solving the first part that is the final volume v2 now we can apply one equation that p1 v1 over t1 is equals to p2 v2 over t2 now here t1 and t2 is same so it will go into cancel it out and we'll get p1 v1 is equals to p2 v2 p1 v1 is equal to p2 v2 p1 v1 is equal to p2 2 to calculate v2 we have to first calculate the initial volume v1 for that will be applying the idle gas equation because the gas behaves like an idle gas so we can apply p1 v1 is equals to n r u t1 where r u is a universal gas constant and its value it's constant and its value we have 8 .314 kilo pascal meter cube over kilo mole kelvin this is a unit of ru now we're going to plug all these value here b1 we have you to put it into kilo pascal so 50 .66 0 .66 kv1 we have to calculate is equal to in moles we have to two two moles times ru we have 8 .314 kilo kilo pascal meter cube over kilo mal kelvin times t1 so t1 we have 298 kelvin but here we have to change the units because this is in kilo mole and this is in moles so we have to divide it with thousand to convert the unit in kilo mole now the units are balanced and we'll get the volume v1 in meter cube so from here we'll get the volume v1 as 0 .0978 meter cube now we're going to plug these values here to calculate to final volume v2 so p1 we have 0 .5 atm now we can put the units in atm because it will go to cancel out so it's a tm and v1 we have 0 .078 meter cube is equals to p2 we have 1 .25 a tm and v2 we have to calculate so this atm atm will cancel out so unit are balanced here and will get the final volume v2 as from here 0 .03912 meter cube.

04:05 So this is the final answer for the a part.

04:09 Now next we'll be solving the b part...

Question

TWO (2) moles of monoatomic gas initially at 25°C and 0.5 atm is compressed isothermally to 1.25 atm. If the gas behaves like an ideal gas, compute:i.the final volume of the gas(6 marks)ii.heat lost during compression

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