Which graph correctly represents the relationship between volume and temperature for an ideal gas at constant pressure and fixed mass?

Step 1: Understand the definition of angular frequency. Angular frequency () is the rate of change of phase. For a complete oscillation, the phase changes by 2 radians over a time period T. Step 2: Apply the formula for angular frequency. The formula for angular frequency is given by: = change in phasetime taken Given that the change in phase is 2 and the time taken is T: = (2)/(T) Step 3: Compare with the given options. The calculated angular frequency matches option D. The final answer is D) = (2)/(T). --- Step 1: Understand the question and relevant gas law. The question asks for the correct graph representing the relationship between volume (V) and temperature for an ideal gas at constant pressure and fixed mass. This describes Charles's Law. Step 2: State Charles's Law. Charles's Law states that for a fixed mass of gas at constant pressure, the volume (V) is directly proportional to its absolute temperature (T_K). V T_K This can be written as V = k T_K, where k is a constant. Step 3: Relate absolute temperature to Celsius temperature. Absolute temperature (T_K) is related to Celsius temperature (t_C) by the formula: T_K = t_C + 273.15 Substituting this into Charles's Law: V = k(t_C + 273.15) This equation shows a linear relationship between V and t_C. Step 4: Analyze the graph's characteristics. The graph of V versus t_C should be a straight line. When t_C = -273.15^ C (absolute zero), the volume V becomes zero: V = k(-273.15 + 273.15) = k(0) = 0 So, the straight line graph should extrapolate to V=0 at t_C = -273.15^ C. Step 5: Evaluate the given options. Option A shows a straight line graph of V versus t_C that extrapolates to V=0 at -273^ C. This is consistent with Charles's Law. Option B shows a curved graph, which is incorrect for the relationship between V and t_C. The final answer is A. Send me the next one 📸