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The behaviour of ideal gas is goverened by various gas laws which are described by mathematical statements as given below: ( i ) PV=k (constant) at constant n and T ( ii ) V//T=k_(2) (constant) at constant n and P ( iii ) V//n=k_(3) (constant) at constant T and P ( iv ) PV=nRT ( v ) P//T=k_(4) (constant) at constant n and V Answer the following A cylinder of 10 L capacity at 300 K containing the gas is used to fill balloons till finally the cylinder recorded a pressure of 10 m bar. The number of He atoms still present in the cylinder is

A train A crosses a station with a speed of 40 m/s and whitles a short pulse of natural frequency n_0=596Hz another train B is approaching towards the same station with the same speed along a parallel track, Two track are d=99m apart. When train A whistles. train B is 152 m away from the station as shown in Fig. If velocity of sound in air is v=300(m)/(s) . calculate frequency of the pulse heard by driver of train B.

A cylindrical container has insulating wall and an insulating piston which can freely move up and down without any friction. It contains a mixture of ideal gases. Originally the gas is at atmospheric pressure P_(0) and temperature (T_(0)) . A tap positioned above the container is opened and it supplies water at a constant rate of (dm)/(dt)= 0.25 kg//s . The water collects above the piston in the container and the gas compresses. The tap is kept open till the temperature of the gas is doubled. During the process the T vs (1)/(V) graph for the gas was recorded and found to be a parabola with its vertex at origin as shown in the graph. Area of piston A = 1.515 xx 10^(-3) m^(2) and atmospheric pressure = 10^(5) N//m^(2) (a) Find the ratio of V_(rms) and speed of sound in the gaseous mixture. (b) For how much time the tap was kept open?

The accountant of a firm finds that the Trial Balance as on 31st March, 2019 is out by an excess debit of Rs. 283. He placed the amount in the Suspense Account. In the first week of April, 2019, he discovered the following errors. Pass the Journal entries necessary to rectify these errors and show the Suspense Account as it would appear at the end of the week. Have you any comment to make? (i) Cash paid to Amar Nath, Rs. 75, was posted to the credit of Amar Singh's Account as Rs. 57. (ii) Discount allowed by Brijesh of Rs. 5 was not entered in the Cash Book but Brijesh stands debited correctly. (iii) No entry was made for goods worth Rs. 40 taken away by proprietor for personal use. (iv) Rs. 500 received from Jhaveri Bros. for interest on loan advanced to them were recorded in the Cash Book. But the entry was not posted in the Ledger. (v) The total of Returns Outward Book was short by Rs. 100. [Hint: At the end of the week, the Suspense Account will be showing a debit balance of Rs. 190. It means that there are still some errors left undetected.]