In an attempt to determine an accurate value of the gas constant, r, a student heated a container of volume 20.000 dm3 filled with 0.251 32 g of helium gas to 500 °c and measured the pressure as 206.402 cm in a manometer filled with water at 25 °c. calculate the value of r from these data. the mass density of water at 25 °c is 0.997 07 g cm−3.

One hazard of space travel is debris left by previous missions. there are several thousand masses large enough to detect by radar orbiting the earth, but there are far greater numbers of very small masses such as flakes of paint. calculate the force exerted by a 0.110 mg chip of paint that strikes a space shuttle window at a relative speed of 5.00 ✕ 103 m/s and sticks, given the collision lasts 6.00 ✕ 10-8 s. such a collision chipped the window of the ill-fated challenger in june 1983, causing $50,000 of damage.