Hi budak - welcome to the board. Just a suggestion, but a better title to your thread would help.
1. Calculate the density of air inside the compression chamber just prior to the start of compression using the ideal gas law. Note that the total mass of air in the cylinder is simply density times volume.
rho = ?
2. Do you know how to apply the polytropic formula? Note the exponent, n is given, so you should be able to find the final conditions (ie: final state) of the air given the inlet pressure, inlet temperature and discharge pressure. Can you find the discharge temperature? If so, you have the final state.
T(final) = ?
3. If you have the final state, you can apply ideal gas law to find density for the final state. Since you've been given the clearance volume as a percentage of total volume, you should also be able to calculate the percentage of air in the clearance volume that stays inside the chamber after compression. This percentage of mass does not exit the compressor. The rest of the air leaves the compressor, so this is the percentage of air which is displaced by each stroke. Now you have (% displaced).
% displaced = ?
4. On the intake stroke, just assume this small mass of air re-expands back to the inlet conditions, so you can neglect this small mass of air after you do the compression stroke calculation in 3 above.
5. Calculate the mass of air that must be displaced with each stroke in order to get the total throughput.
Mass per stroke needed = ?
6. Find total displacement of cylinder from % displaced and mass per stroke as found above.
Volume of cyl = ?
7. Find bore and stroke from stroke to bore ratio and volume calculated in 6.
Bore = ?
Stroke = ?
hope that helps.