Question

A 1.0 m³ tank, initially filled with 103. kPa, 300. K air, is connected to a source of air at 1,500. kPa, 300. K. The tank slowly fills until it is at the same pressure. If the temperature is maintained at 300. K throughout this transient process, what is the total heat transfer required? (You can assume air is an ideal gas.)

Answer 1

Answer – Given, volume, V = 1.0 m³, P1 = 103.0 kPa, P2 = 1500.0 kPa , T = 300 K

And we need to calculate the total heat transfer required

From the give data we can calculate the work using the formula

W = -deltan*RT*lnP1/P2)

We need to calculate moles first

We need to volume in L

So, 1.0 m³ = 1000 dm³ = 1000 L

P in atm –

1 kPa = 0.00987 atm

So, 103 kPa = ?

= 1.02 atm

Now using the Ideal gas law

n = PV/RT

= 1.02 atm*1000 L / 0.0821* 300 K

= 41.4 moles

Moles of air –

P = 1500 kPa = 14.78 atm

n = 14.8 atm*1000 L / 0.0821* 300 K

= 600.9 moles

Deltan =600.9 -41.4 = 559.5 moles

So work

w = - 559.5 * 8.314 J/mol.K * 300 K * ln 103/1500

     = 1.246*10⁴ J

We are given constant temperature, so ΔE = 0

Then w = -q

So, heat , q = -w

                   = - 1.246*10⁴ J

The total heat transfer required is - 1.246*10⁴ J