Solving Pressure and Force in Gas Experiments

AI Thread Summary
The discussion focuses on solving pressure and force calculations in gas experiments. For part (a), the slope of the P vs. T graph is given as 235 Pa/L, and the pressure at 0 degrees Celsius can be determined using the ideal gas law. In part (b), with a syringe radius of 5 mm and an internal pressure of 2.00 x 10^5 Pa, the force exerted by the gas on the plunger can be calculated, along with the force needed to maintain equilibrium. Part (c) compares two groups performing P vs. V experiments with different initial volumes, leading to a discussion on how to express the slope of their graphs and the differing quantities involved. The overall approach emphasizes understanding the relationships between pressure, volume, and temperature in gas behavior.
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Homework Statement



a) Suppose that in the experiment involving P vs. T, the slope of the graph of P vs. T is 235 Pa/L/ Determine the pressure of the gas at T = 0 degrees celsius.

b) The radius of the syringe is approximately 5 mm. Suppose that the pressure of the gas inside the syringe is 2.00 x 10^5 Pa. Determine the force exerted by the gas on the plunger and the force exerted by your hand on the plunger to hold it in equilibrium.

c) Two groups perform the part of the lab involving P vs. V but start with different volumes of air in the syringe. The temperatures of the gases are the same for both groups. Group A attached the pressure sensor when the volume of the syringe is 20 ml and group B when the volume is 10 ml. Using Eq. (1) determine an expression for the slope of these graphs. Identify which quantities in this expression are different for the two groups and use this to relate the slopes of the graphs of P vs. 1/V for the two groups.


Homework Equations


PV= nRT


The Attempt at a Solution

 
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You know the ideal gas law how about dividing it by V then you have the slope. Also the important part of this question is to calculate in K 0 deg cel. is 273.14K
 
So the equation I would use is PV = nRT/V ? Is this the right direction?
 
Try P=(nR/V) T.

The slope is (nR/V).
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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